2018/12/18 by Rida Benhaddou, Qing Liu, Benhaddou, Rida +1
Computer Science · Economics, Econometrics and Finance · #62G05 #62G08 #62G20 #FOS: Mathematics #Financial Risk and Volatility Modeling #Image and Signal Denoising Methods #Statistics Theory (math.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1812.07479
openalex publication_date 2018/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We look into the minimax results for the anisotropic two-dimensional functional deconvolution model with the two-parameter fractional Gaussian noise. We derive the lower bounds for the Lp-risk, 1 ≤ p < ∞, and taking advantage of the Riesz poly-potential, we apply a wavelet-vaguelette expansion to de-correlate the anisotropic fractional Gaussian noise. We construct an adaptive wavelet hard-thresholding estimator that attains asymptotically quasi-optimal convergence rates in a wide range of Besov balls. Such convergence rates depend on a delicate balance between the parameters of the Besov balls, the degree of ill-posedness of the convolution operator and the parameters of the fractional Gaussian noise. A limited simulations study confirms theoretical claims of the paper. The proposed approach is extended to the general r-dimensional case, with r> 2, and the corresponding convergence rates do not suffer from the curse of dimensionality.